Answer:
A. 1/2 = 0.5
Step-by-step explanation:
We are given that the couple stops bearing a child until they get two boys.
Now, if the couple bears less than 2 girls.
Then the possible cases are: BB, BGB and GBB.
As the probability of the child being a boy = 0.5
Thus, the probability of the child being a girl = 1 - 0.5 = 0.5.
Hence, the probability that the couple bears less than 2 girls = sum of probabilities of BB, BGB and GBB.
i.e. Probability of less than 2 girls =
+
+ ![(\frac{1}{2})^{3}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B3%7D)
i.e. Probability =
i.e. Probability = ![\frac{1}{4} +\frac{2}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B2%7D%7B8%7D)
i.e. Probability = ![\frac{1}{4} +\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B1%7D%7B4%7D)
i.e. Probability = ![\frac{2}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B4%7D)
i.e. Probability = ![\frac{1}{2}= 0.5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%200.5)
Thus, the probability of less than 2 girls = 0.5
So, the probability of atleast 2 girls = 1 - Probability of less than 2 girls
i.e. The probability of atleast 2 girls = 1 - 0.5 = 0.5
Hence, the probability that the couple has atleast 2 girls is 0.5 = 1/2.